Problem: Ikta has an extraordinary feeling for undirected graphs. Ikta likes the undirected graph G and its two-point s, t pair (G, s, t) that has the greatest "beauty". The "beauty" of a pair (G, s, t) is the edge e = \\ {u, v \\} (u and v are two different points of G), and the shortest path from s to t in G. Is the number of things whose length is greater than the length of the shortest path from s to t in the undirected graph with g plus e.

Your job is to write a program that seeks its "beauty" given a pair (G, s, t).



Input

The input is given in the following format.

> N M s t
> x1 y1
> ...
> xi yi
> ...
> xM yM
>

First, the number of vertices, the number of edges, and the integers N, M, s, t representing the two vertices of the undirected graph are input. From the 2nd line to the M + 1th line, two vertices connected by edges are input. (However, let the set of G vertices be \\ {1, ..., N \\}.)

Constraints

Each variable being input satisfies the following constraints.

* 2 ≤ N ≤ 100,000
* 1 ≤ M ≤ 300,000
* 1 ≤ s, t, xi, yi ≤ N
* Different from s and t
* Guaranteed to reach t from s

Output

When the given graph is G, output the "beauty" of the set (G, s, t) in one line.

Examples

Input

3 2 1 3
1 2
2 3


Output

1


Input

9 8 7 8
2 6
4 9
8 6
9 2
3 8
1 8
8 5
7 9


Output

7


Input

4 3 1 4
1 2
3 4
4 1


Output

0


Input

9 7 8 9
9 6
6 5
3 6
3 7
2 5
8 5
1 4


Output

2

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<int> vint;
typedef pair<int,int> pint;
typedef vector<pint> vpint;
#define rep(i,n) for(int i=0;i<(n);i++)
#define REP(i,n) for(int i=n-1;i>=(0);i--)
#define reps(i,f,n) for(int i=(f);i<(n);i++)
#define each(it,v) for(__typeof((v).begin()) it=(v).begin();it!=(v).end();it++)
#define all(v) (v).begin(),(v).end()
#define eall(v) unique(all(v), v.end())
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define chmax(a, b) a = (((a)<(b)) ? (b) : (a))
#define chmin(a, b) a = (((a)>(b)) ? (b) : (a))
const int MOD = 1e9 + 7;
const int INF = 1e9;
const ll INFF = 1e18;

const int MAX_N = 100010;
vector<pair<int, int> > G[MAX_N];
vector<int> dijkstra(int start){
	vector<int> dist(MAX_N, INF);
	dist[start] = 0;//dist[i] :=???start->i?????§??????????????¢
	priority_queue<pair<int, int>, vector<pair<int, int> >, greater<pair<int, int> > >  que;
	que.push(make_pair(0, start));
	while(!que.empty()){
		int cost; int u;//????????§???????????£????????? ?????¨?????????
		cost = que.top().first, u = que.top().second;
		que.pop();
		if(dist[u] < cost) continue;
		for (auto tmp : G[u]){
			int v = tmp.first; int time = tmp.second;//??£??\???????????? ?????????????????§????????????
			if(dist[v] > dist[u] + time){//u->v
				dist[v] = dist[u] + time;
				que.push(make_pair(dist[v], v));
			}
		}
	}
	return dist;
}

int N, M, s, t;
int x[300010], y[300010];
set<int> dists[100010], distg[100010];

int main(void){
	scanf("%d %d %d %d", &N, &M, &s, &t);
	s--, t--;
	rep(i, M) scanf("%d %d", &x[i], &y[i]);
	rep(i, M) x[i]--, y[i]--;
	rep(i, M) G[x[i]].pb(mp(y[i], 1)), G[y[i]].pb(mp(x[i], 1));
	auto start = dijkstra(s);
	auto goal  = dijkstra(t);

	rep(i, N) if(start[i] != INF) dists[start[i]].insert(i);
	rep(i, N) if(goal[i]  != INF) distg[goal[i]].insert(i);
	// set<pair<int, int> > ans;
	ll ans = 0;
	int len = start[t];
	// printf("len %d\n", len);
	rep(i, len - 1){
		int d1 = i;
		int d2 = (len - 2) - i;
		// printf("d1 %d d2 %d\n", d1, d2);
		for(auto u : dists[d1]){ // s -> u ??? ?????¢ d1
			// u ??¨ v?????°????????°??????
			if(distg[d2].count(u) == 0) ans += distg[d2].size();
			else ans += distg[d2].size() - 1;
			/*
			for(auto v : distg[d2]){
				// printf("%d %d\n", u, v);
				if(u != v) ans.insert(mp(min(u, v), max(u, v)));
			}
			*/
		}
	}
	// printf("%d\n", (int)ans.size());
	printf("%lld\n", ans);
	return 0;
}